热声固耦合问题多参数识别中解的唯一性和算法研究  

Research on the uniqueness and algorithm of multi-parameter identification in coupling thermal acoustic and solid problem

作　　者：朱丽艳 邓又军 魏东[2] 桂业伟[2] ZHU LiYan;DENG YouJun;WEI Dong;GUI YeWei(School of Mathematics and Statistics,Central South University,Changsha 410083,China;State Key Laboratory of Aerodynamics,China Aerodynamics Research and Development Center,Mianyang 621000,China)

机构地区：[1]中南大学数学与统计学院,长沙410083 [2]中国空气动力研究与发展中心空气动力学国家重点实验室,绵阳621000

出　　处：《中国科学：技术科学》2023年第3期330-340,共11页Scientia Sinica(Technologica)

基　　金：国家重点研发计划(编号:2019YFA0405202);国家自然科学基金(批准号:11971487,11972361);湖南省自然科学基金(编号:2020JJ2038);四川省科技计划(编号:2020JDJQ0031)资助项目。

摘　　要：本文研究了一类热声固多物理场耦合中的初边值识别问题,建立了基于超声回波时间测量的固体结构表面热流和尺寸的多参数同时识别模型.利用热传导方程的极值原理,证明了耦合问题多参数识别中解的唯一性,为超声同时测温测厚等工程应用提供了理论支撑.在数值求解正问题的基础上,将反问题重新表述为由偏微分方程约束的优化问题.将共轭梯度法反演热流和最速下降法反演厚度相结合,发展了多参数识别问题的交替迭代算法,并通过严格的收敛性分析,给出了交替迭代算法的收敛性条件,证明了算法的全局收敛性.最后通过设计数值算例,验证了本算法的可靠性和可行性,并对比了仅识别热流的单参数识别算法,验证了本算法在精度方面的提高.In the coupled thermal-acoustic solid field,we consider the identification problem of initial boundary value from the boundary measurements of temperature and ultrasonic propagation time to reconstruct the boundary heat flux and thickness of a solid structure simultaneously.Through rigorous theoretical analysis,the uniqueness of the simultaneous identification is demonstrated,which provides theoretical support for engineering applications.By reformulating an inverse problem as an optimization problem and deriving the adjoint equation,we propose an efficient alternating iteration algorithm for solving the inverse problem.Rigorous convergence analysis of the proposed algorithm is performed.Finally,the reliability and feasibility of the algorithm are verified via numerical examples,and the algorithm’s accuracy is verified by comparing it with a single-parameter identification algorithm that only identifies heat flux.

关 键 词：热声固耦合 多参数反演 反问题唯一性 交替迭代算法 收敛性分析 

分 类 号：TB5[理学—物理]